V.8:2 (74-77): Volatility skews by Andrew Sterge

V.8:2 (74-77): Volatility skews by Andrew Sterge
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Volatility skews by Andrew Sterge

It is inevitable that relative mispricings occur among many different options on a single underlying instrument. It is possible to exploit these mispricings using the Black-Scholes theory of option valuation, despite risk and the inherent flaws in the model. This can be done by trading spreads in which theoretically underpriced options are bought and theoretically overpriced options are sold. Analysis of virtually any class of option prices reveals that the options do not all trade at the same implied volatility.

This is counterintuitive, because implied volatilities on a single underlying instrument are supposed to measure the same parameter that is, the market's perception of that instrument's volatility over the remaining life of the option. Implied volatility of options with the same expiration date, considered a function of strike price, is called the volatility skew. Since options with different strike prices cannot be compared strictly on the basis of price, their volatility skews become a convenient way to represent the relative richness or cheapness of the options.

Take, for example, October 16, 1989, which was a particularly rich day for volatility skews, as demonstrated by the three different types of skews in Figure 1. Note how the out-of-the-money options for cattle, Eurodollar and bond futures all traded at higher implied volatilities than at-the-money options for these contracts. This implies that out-of-the-money options are overpriced relative to at-the-money options.




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